Positive solutions to singular fractional differential system with coupled boundary conditions

Miller, 1993 Podlubny, 1999, Fractional differential equations, Vol. 198 Samko, 1993 Agarwal, 2010, Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations, J Math Anal Appl, 371, 57, 10.1016/j.jmaa.2010.04.034 Ahmad, 2009, Existence of solutions for nonlocal boundary value problems of higher-order nonlinear fractional differential equations, Abstr Appl Anal, 2009, 9, 10.1155/2009/494720 Bai, 2010, On positive solutions of a nonlocal fractional boundary value problem, Nonlinear Anal TMA, 72, 916, 10.1016/j.na.2009.07.033 Caballero, 2011, On existence and uniqueness of positive solutions to a class of fractional boundary value problems, Bound Value Prob, 2011, 25, 10.1186/1687-2770-2011-25 El-Shahed, 2007, Positive solutions for boundary value problems of nonlinear fractional differential equation, Abstr Appl Anal, 2007, 8, 10.1155/2007/10368 Goodrich, 2010, Existence of a positive solution to a class of fractional differential equations, Appl Math Lett, 23, 1050, 10.1016/j.aml.2010.04.035 McRae, 2009, Monotone iterative technique and existence results for fractional differential equations, Nonlinear Anal TMA, 71, 6093, 10.1016/j.na.2009.05.074 Wang, 2011, Positive solutions of the three-point boundary value problem for fractional-order differential equations with an advanced argument, Adv Difference Equ, 2011, 2, 10.1186/1687-1847-2011-2 Xu, 2012, The positive properties of Green’s function for three point boundary value problems of nonlinear fractional differential equations and its applications, Commun Nonlinear Sci Numer Simul, 17, 1555, 10.1016/j.cnsns.2011.08.032 Zhang, 2000, The existence of a positive solution for a nonlinear fractional differential equation, J Math Anal Appl, 252, 804, 10.1006/jmaa.2000.7123 Zhang, 2012, Multiple positive solutions of a singular fractional differential equation with negatively perturbed term, Math Comput Model, 55, 1263, 10.1016/j.mcm.2011.10.006 Zhou, 2012, Multiple positive solutions for nonlinear semipositone fractional differential equations, Discrete Dyn Nat Soc, 2012, 10 Ahmad, 2010, Existence and uniqueness of solutions for coupled systems of higher-order nonlinear fractional differential equations, Fixed Point Theory Appl, 2010, 17, 10.1155/2010/364560 Ahmad, 2009, Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Comput Math Appl, 58, 1838, 10.1016/j.camwa.2009.07.091 Bai, 2004, The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations, Appl Math Comput, 150, 611, 10.1016/S0096-3003(03)00294-7 Goodrich, 2011, Existence of a positive solution to systems of differential equations of fractional order, Comput Math Appl, 62, 1251, 10.1016/j.camwa.2011.02.039 Jiang, 2012, Solvability for a coupled system of fractional differential equations at resonance, Nonlinear Anal RWA, 13, 2285, 10.1016/j.nonrwa.2012.01.023 Rehman, 2011, A note on boundary value problems for a coupled system of fractional differential equations, Comput Math Appl, 61, 2630, 10.1016/j.camwa.2011.03.009 Salem, 2008, On the existence of continuous solutions for a singular system of non-linear fractional differential equations, Appl Math Comput, 198, 445, 10.1016/j.amc.2007.08.063 Su, 2009, Boundary value problem for a coupled system of nonlinear fractional differential equations, Appl Math Lett, 22, 64, 10.1016/j.aml.2008.03.001 Wang, 2010, Positive solution to nonzero boundary values problem for a coupled system of nonlinear fractional differential equations, Int J Differ Equ, 2010, 12 Yuan, 2012, Two positive solutions for (n-1,1)-type semipositone integral boundary value problems for coupled systems of nonlinear fractional differential equations, Commun Nonlinear Sci Numer Simul, 17, 930, 10.1016/j.cnsns.2011.06.008 Zhang, 2011, Existence results for a coupled system of nonlinear fractional three-point boundary value problems at resonance, Comput Math Appl, 61, 1032, 10.1016/j.camwa.2010.12.053 Nelson, 2002, Mathematical analysis of delay differential equation models of HIV-1 infection, Math Biosci, 179, 73, 10.1016/S0025-5564(02)00099-8 Wang, 2006, Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells, Math Biosci, 200, 44, 10.1016/j.mbs.2005.12.026 Culshaw, 2000, A delay-differential equation model of HIV infection of CD4+ T-cells, Math Biosci, 165, 27, 10.1016/S0025-5564(00)00006-7 Tuckwell, 2004, On the behavior of solutions in viral dynamical models, Biosystems, 73, 157, 10.1016/j.biosystems.2003.11.004 Merdan, 2010, Homotopy perturbation method for solving viral dynamical model, CÜ Fen-Edebiyat Fakültesi, Fen Bilimleri Dergisi, 31, 65 Petrovic, 2005, On a mathematical model of a human root dentin, Dent Mater, 21, 125, 10.1016/j.dental.2004.01.004 Perelson, 1989, Modeling the interaction of the immune system with HIV, Vol. 83, 350 Perelson, 1993, Dynamics of HIV infection of CD4+ T cells, Math Biosci, 114, 81, 10.1016/0025-5564(93)90043-A Agmon, 1964, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Commun Pure Appl Math, 17, 35, 10.1002/cpa.3160170104 Amann, 1988, Parabolic evolution equations and nonlinear boundary conditions, J Differ Equ, 72, 201, 10.1016/0022-0396(88)90156-8 Aronson, 1978, A comparison method for stability analysis of nonlinear parabolic problems, SIAM Rev, 20, 245, 10.1137/1020038 Cardanobile, 2009, Parabolic systems with coupled boundary conditions, J Differ Equ, 247, 1229, 10.1016/j.jde.2009.04.013 Delgado, 2010, On a parabolic-elliptic chemotactic model with coupled boundary conditions, Nonlinear Anal RWA, 11, 3884, 10.1016/j.nonrwa.2010.02.016 Ferreira, 2006, Non-simultaneous quenching in a system of heat equations coupled at the boundary, Z Angew Math Phys, 57, 586, 10.1007/s00033-005-0003-z Leung, 1982, A semilinear reaction–diffusion prey–predator system with nonlinear coupled boundary conditions: equilibrium and stability, Indiana Univ Math J, 31, 223, 10.1512/iumj.1982.31.31020 Mikhailov, 1973, General solutions of the diffusion equations coupled at boundary conditions, Int J Heat Mass Transfer, 16, 2155, 10.1016/0017-9310(73)90003-3 Pao, 2002, Finite difference reaction-diffusion systems with coupled boundary conditions and time delays, J Math Anal Appl, 272, 407, 10.1016/S0022-247X(02)00145-2 Rossi, 1997, The blow-up rate for a system of heat equations with non-trivial coupling at the boundary, Math Methods Appl Sci, 20, 1, 10.1002/(SICI)1099-1476(19970110)20:1<1::AID-MMA843>3.0.CO;2-E Wang, 2002, Doubly nonlinear degenerate parabolic systems with coupled nonlinear boundary conditions, J Differ Equ, 182, 431, 10.1006/jdeq.2001.4101 Wang, 1999, The blow-up rate for a system of heat equations completely coupled in the boundary conditions, Nonlinear Anal TMA, 35, 389, 10.1016/S0362-546X(98)00010-8 Krasnoselskii, 1964 Guo, 1988